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@article{ast,
	Author = {Armstrong, D. and Stump, C. and Thomas, H.},
	Date-Modified = {2017-05-20 06:12:10 +0000},
	Doi = {10.1090/s0002-9947-2013-05729-7 },
	Journal = {Trans. Amer. Math. Soc},
	Pages = {4121--4151},
	Title = {A uniform bijection between nonnesting and noncrossing partitions},
	Volume = {365},
	Year = {2013}}

@book{bjornerbrenti,
	Author = {Bj{\"o}rner, A. and Brenti, F.},
	Date-Modified = {2017-05-20 06:12:29 +0000},
	Publisher = {Springer-Verlag},
	Title = {Combinatorics of {C}oxeter Groups},
	Year = {2005}}

@article{brouwer1974period,
	Author = {Brouwer, A. and Schrijver, L.},
	Date-Modified = {2017-05-20 06:12:52 +0000},
	Journal = {Stichting Mathematisch Centrum. Zuivere Wiskunde},
	Pages = {1--13},
	Title = {On the period of an operator, defined on antichains},
	Volume = {ZW 24/74},
	Year = {1974}}

@article{cameronfonder,
	Author = {Cameron, P. and Fon{-}der{-}Flaass, D.},
	Date-Modified = {2017-05-20 06:13:30 +0000},
	Doi = {10.1016/0195-6698(95)90036-5 },
	Journal = {European J. Combin.},
	Pages = {545--554},
	Title = {Orbits of antichains revisited},
	Volume = {16},
	Year = {1995}}

@misc{develin2015toric,
	Author = {Develin, M. and Macauley, M. and Reiner, V.},
	Note = {{\em Trans. Amer. Math. Soc.}, In press, 2015.},
	Title = {Toric partial orders},
	Year = {2015}}

@article{efgjmpr,
	Author = {Einstein, D. and Farber, M. and Gunawan, E. and Joseph, M. and Macauley, M. and Propp, J. and Rubinstein-Salzedo, S.},
	Date-Modified = {2017-05-20 06:16:07 +0000},
	Journal = {Electron. J. Combin.},
	Number = {3},
	Pages = {Art. \#P3.52},
	Title = {Noncrossing partitions, toggles, and homomesies},
	Url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i3p52},
	Volume = {23},
	Year = {2016}}

@misc{einpropp,
	Archiveprefix = {arXiv},
	Author = {Einstein, D. and Propp, J.},
	Eprint = {1310.5294},
	Title = {Combinatorial, piecewise-linear, and birational homomesy for products of two chains},
	Year = {2013}}

@article{eriksson2009conjugacy,
	Author = {Eriksson, H. and Eriksson, K.},
	Journal = {Electron. J. Combin.},
	Number = {2},
	Pages = {\#R4},
	Title = {Conjugacy of {C}oxeter elements},
	Volume = {16},
	Year = {2009}}

@misc{shahrzad,
	Archiveprefix = {arXiv},
	Author = {Haddadan, S.},
	Date-Modified = {2017-05-20 06:23:27 +0000},
	Eprint = {1410.4819},
	Title = {Some Instances of Homomesy Among Ideals of Posets},
	Year = {2016}}

@article{heitsch2015counting,
	Author = {Heitsch, C.},
	Note = {In preparation},
	Title = {Counting orbits under {K}reweras complementation}}

@misc{indepsetspaper,
	Archiveprefix = {arXiv},
	Author = {Joseph, M. and Roby, T.},
	Eprint = {1701.04956},
	Title = {Toggling independent sets of a path graph},
	Year = {2017}}

@article{kleiner2007admissible,
	Author = {Kleiner, M. and Pelley, A.},
	Doi = {10.1093/imrn/rnm013},
	Fjournal = {International Mathematics Research Notices. IMRN},
	Issn = {1073-7928},
	Journal = {Int. Math. Res. Not. IMRN},
	Mrclass = {16G20 (05E15)},
	Mrnumber = {2338197 (2008f:16035)},
	Mrreviewer = {Alistair Savage},
	Number = {4},
	Pages = {Art. ID rnm013, 28},
	Title = {Admissible sequences, preprojective representations of quivers, and reduced words in the {W}eyl group of a {K}ac-{M}oody algebra},
	Url = {http://dx.doi.org/10.1093/imrn/rnm013},
	Year = {2007},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/imrn/rnm013}}

@article{kreweras1972sur,
	Author = {Kreweras, G.},
	Fjournal = {Discrete Mathematics},
	Issn = {0012-365X},
	Journal = {Discrete Math.},
	Mrclass = {05A17 (06A20)},
	Mrnumber = {0309747 (46 \#8852)},
	Mrreviewer = {R. J. Wilson},
	Number = {4},
	Pages = {333--350},
	Title = {Sur les partitions non crois\'ees d'un cycle},
	Volume = {1},
	Year = {1972}}

@article{macauley2011admissible,
	Author = {Macauley, M. and Mortveit, H.},
	Journal = {Electron. J. Combin.},
	Number = {1},
	Pages = {\#R197},
	Title = {Posets from admissible {C}oxeter sequences},
	Volume = {18},
	Year = {2011}}

@article{mccammond2006noncrossing,
	Author = {McCammond, J.},
	Journal = {Amer. Math. Monthly},
	Number = {7},
	Pages = {598-610},
	Title = {Noncrossing partitions in surprising locations},
	Volume = {113},
	Year = {2006}}

@article{panyushev,
	Author = {Panyushev, D.},
	Date-Modified = {2017-05-20 06:17:27 +0000},
	Doi = {10.1016/j.ejc.2008.03.009 },
	Journal = {European J. Combin.},
	Pages = {586--594},
	Title = {On orbits of antichains of positive roots},
	Volume = {30},
	Year = {2009}}

@book{peterseneulerian,
	Author = {Petersen, T. K.},
	Date-Modified = {2017-05-20 06:17:51 +0000},
	Publisher = {Springer},
	Title = {Eulerian Numbers},
	Year = {2015}}

@article{pretzel1986reorienting,
	Author = {Pretzel, O.},
	Journal = {Order},
	Number = {2},
	Pages = {135--153},
	Title = {On reorienting graphs by pushing down maximal vertices},
	Volume = {3},
	Year = {1986}}

@article{propproby,
	Author = {Propp, J. and Roby, T.},
	Date-Modified = {2017-05-20 06:18:35 +0000},
	Journal = {Electron. J. Combin.},
	Number = {3},
	Pages = {Art. \#P3.4},
	Title = {Homomesy in Products of Two Chains},
	Url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p4},
	Volume = {22},
	Year = {2015}}

@article{csp,
	Author = {Reiner, V. and Stanton, D. and White, D.},
	Date-Modified = {2017-05-20 06:19:18 +0000},
	Doi = {10.1016/j.jcta.2004.04.009 },
	Journal = {J. Combin. Theory Ser. A},
	Pages = {17--50},
	Title = {The cyclic sieving phenomenon},
	Volume = {108},
	Year = {2004}}

@incollection{robydac,
	Author = {Roby, T.},
	Booktitle = {Recent Trends in Combinatorics},
	Date-Modified = {2017-05-20 06:19:54 +0000},
	Note = {Also available at \href{http://www.math.uconn.edu/~troby/homomesyIMA2015Revised.pdf}{URL}},
	Pages = {619--652},
	Publisher = {Springer},
	Title = {Dynamical algebraic combinatorics and the homomesy phenomenon},
	Year = {2016}}

@article{cspsagan,
	Author = {Sagan, B.},
	Journal = {London Math. Soc. Lecture Note Ser},
	Note = {Also available at \arxiv{1008.0790v3}.},
	Pages = {183-233},
	Title = {The Cyclic Sieving Phenomenon: A Survey},
	Volume = {392},
	Year = {2011}}

@article{shi1997enumeration,
	Author = {Shi, J.},
	Coden = {JAOME7},
	Doi = {10.1023/A:1008695121783},
	Fjournal = {Journal of Algebraic Combinatorics. An International Journal},
	Issn = {0925-9899},
	Journal = {J. Algebraic Combin.},
	Mrclass = {20F55 (05C25)},
	Mrnumber = {1436533 (98d:20048)},
	Mrreviewer = {Luis Paris},
	Number = {2},
	Pages = {161--171},
	Title = {The enumeration of {C}oxeter elements},
	Url = {http://dx.doi.org/10.1023/A:1008695121783},
	Volume = {6},
	Year = {1997},
	Bdsk-Url-1 = {http://dx.doi.org/10.1023/A:1008695121783}}

@article{simion91structure,
	Author = {Simion, R. and Ullman, D.},
	Journal = {Discrete Math.},
	Pages = {193--206},
	Title = {On the structure of the lattice of noncrossing partitions},
	Volume = {98},
	Year = {1991}}

@article{speyer2009powers,
	Author = {Speyer, D.},
	Journal = {Proc. Amer. Math. Soc.},
	Pages = {1295--1302},
	Title = {Powers of {C}oxeter Elements in Infinite Groups are Reduced},
	Volume = {137},
	Year = {2009}}

@article{stanley1973acyclic,
	Author = {Stanley, R.},
	Journal = {Discrete Math.},
	Pages = {171--178},
	Title = {Acyclic orientations of graphs},
	Volume = {5},
	Year = {1973}}

@book{ec1ed2,
	Author = {Stanley, R. P.},
	Date-Modified = {2017-05-20 06:21:37 +0000},
	Edition = {2},
	Note = {Also available at \href{http://math.mit.edu/~rstan/ec/ec1/}{URL}},
	Publisher = {Cambridge University Press},
	Title = {Enumerative Combinatorics, Vol. 1},
	Year = {2011}}

@book{ec2,
	Author = {Stanley, R.},
	Publisher = {Cambridge University Press},
	Title = {Enumerative combinatorics, volume 2},
	Year = {1999}}

@misc{strikergentog,
	Archiveprefix = {arXiv},
	Author = {Striker, J.},
	Eprint = {1601.03710},
	Title = {Rowmotion and Generalized Toggle Groups},
	Year = {2016}}

@article{strikerRS,
	Author = {Striker, J.},
	Date-Modified = {2017-05-20 06:22:37 +0000},
	Journal = {Electron. J. Combin.},
	Number = {2},
	Pages = {Art. \#P2.57},
	Title = {The toggle group, homomesy, and the {R}azumov-{S}troganov correspondence},
	Url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i2p57},
	Volume = {22},
	Year = {2015}}

@article{strikerwilliams,
	Author = {Striker, J. and Williams, N.},
	Date-Modified = {2017-05-20 06:24:13 +0000},
	Doi = {10.1016/j.ejc.2012.05.003 },
	Journal = {European J. Combin.},
	Pages = {1919--1942},
	Title = {Promotion and rowmotion},
	Volume = {33},
	Year = {2012}}

@article{tutte1954contribution,
	Author = {Tutte, W.},
	Journal = {Canad. J. Math.},
	Pages = {80--91},
	Title = {A contribution to the theory of chromatic polynomials},
	Volume = {6},
	Year = {1954}}

@manual{oeis,
	Author = {N. J. A. Sloane},
	Date-Modified = {2017-05-20 06:21:04 +0000},
	Title = {Online Encyclopedia of Integer Sequences},
	Url = {https://oeis.org/},
	Year = {2016}}

@manual{sage,
	Author = {W. A. Stein and others},
	Date-Modified = {2017-05-20 06:20:49 +0000},
	Organization = {The Sage Development Team},
	Title = {{S}age {M}athematics {S}oftware ({V}ersion 7.3)},
	Url = {http://www.sagemath.org},
	Year = {2016}}